Advanced Calculus  Fundamentals of Mathematics

Advanced Calculus Fundamentals of Mathematics

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and ...
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Geometric Algebra

Pp. 124-138 (15)

Carlos Polanco

Abstract

This chapter intends to be a survey on Exterior Algebra. This algebra is attributed to Hermann Grassmann [Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik, 1842], and it is formed by two operators: the exterior product and inner product. William K. Clifford unified both products under the geometric product operator and David Hestenes improved the geometric and computer aspects of Geometric algebra. Here, we review the main operators and their properties, as well as their application in the representation of lines and planes.

Keywords:

Bivector, Differential forms, Differentiation, Dot product, Dual space, Exterior product, Geometric algebra, Geometric product, Grassmann algebra, Inner product, Norm, Oriented plane, Orthogonal basis, Reflections, Rigid body motions, Rotations.

Affiliation:

Department of Mathematics Faculty of Sciences Universidad Nacional Autónoma de México México City México.